Scale Flow Simulation Research Articles

Risk assessment on the impact of Non-Darcy flow on unconventional well performance.

Nano-pores in unconventional reservoirs can cause deviations from Darcy's law where permeability becomes a strong function of pore size and pore pressure. As pores become smaller, the interaction of gas molecules with the pore walls becomes increasingly dominant compared to interactions between gas molecules. This increases gas mobility leading permeabilities measured in the lab not to be accurate at reservoir conditions. Thus, corrections to Darcy flow may be needed when analyzing well production behavior. This paper demonstrates a novel workflow for modeling the impact of non-Darcy flow regimes (i.e., gas slippage, transition flow and Knudsen diffusion) from pore scale characterization to reservoir scale flow simulation. A stochastic approach is used for uncertainty assessment on non-Darcy corrections needed for methane mobility as pore pressure depletes based on reservoir properties, pore sizes, rock compressibility and compaction. Flow simulations are conducted for a range of scenarios to test the impact on the recovery of an unconventional well. Study is conducted using a commercial simulator since workflow modifies the input to the simulator and does not need a new code development. The workflow is demonstrated using field data and shows that non-Darcy flow regimes can have significant impact by increasing gas mobility at low pore pressures near hydraulic fractures. For the field under study, ignoring non-Darcy flow risks up to 20% lower estimations in cumulative gas production under certain scenarios.

A 6M digital twin for modeling and simulation in subsurface reservoirs

A 6M digital twin for modeling and simulation in subsurface reservoirs

A Simplified Physical Model Construction Method and Gas-Water Micro Scale Flow Simulation in Tight Sandstone Gas Reservoirs

Accuracy defects exist when modeling fluid transport by the classical capillary bundle model for tight porous media. In this study, a three-dimensional simplified physical model construction method was developed for tight sandstone gas reservoirs based on the geological origin, sedimentary compaction and clay mineral-cementation. The idea was to reduce the porosity of the tangent spheres physical model considering the synergistic effect of the above two factors and achieve a simplified model with the same flow ability as the actual tight core. Regarding the wall surface of the simplified physical model as the boundary and using the Lattice Boltzmann (LB) method, the relative permeability curves of gas and water in the simplified model were fitted with experimental results and a synergistic coefficient could be obtained, which we propose for characterizing the synergistic effect of sedimentary compaction and clay mineral-cementation. The simplified physical model and the results simulated by the LB method are verified with the experimental results under indoor experimental conditions, and the two are consistent. Finally, we have carried out a simulation of gas flooding water under conditions of high temperature and high pressure which are consistent with the actual tight sandstone gas reservoir. The simulation results show that both gas and water have relatively stronger seepage ability compared with the results of laboratory experiments. Moreover, the interfacial tension between gas and water is lower, and the swept volume is larger during placement. In addition, the binding ability of the rock surface to the water film adhered to it becomes reduced. The method proposed in this study could indicate high frequency change of pores and throats and used to reflect the seepage resistance caused by frequent collisions with the wall in microscopic numerical simulations of tight sandstone gas reservoirs.

Improved skeleton extraction method considering surface feature of natural micro fractures in unconventional shale/tight reservoirs

Massive micro fractures (MFs) developed in the ultra-tight formations (such as shale/tight reservoirs), which provide preferential channels for the fluids flow. Accurate characterization of such pore-fracture systems and suitable pore network models are the fundamentals of pore structure characterization and micro scale flow simulation. Conventional medial axis (MA) skeleton extraction method cannot preserve the fracture surface feature and connectivity information, which is not suitable for accurate pore scale simulation for these porous media with MFs.In this paper, a new skeleton model was proposed to distinguish MFs from pore space via extraction of surface points set of MFs. In the procedure of points set extraction, we improved the classic “MA based” shrink method to “medial surface (MS) based” method for the MFs characterization through introducing a new set of skeleton points (i.e., surface points and edge points of the micro fractures). The former describes their apertures and the latter is used for collecting connectivity information and determining the extension ranges of the MFs. Comparison of connectivity index, fracture length, Euclidean distance showed enhanced effectiveness and accuracy of the proposed method. The proposed method was applied in four ideal models and one field shale core sample. Results show that the proposed skeleton model can show more comprehensible forms of the real connected junction instead of the conventional ideal model. The extracted skeleton can also satisfy demands of the traditional skeleton extraction model and preserve the topology of the original pore-fracture space. This work proposed a more accurate method for pore-scale modeling in cores with natural MFs, and potentially applicable for pore scale flow simulations for tight/shale reservoirs.

Petrographic characterization to build an accurate rock model using micro-CT: Case study on low-permeable to tight turbidite sandstone from Eocene Shahejie Formation

Pore scale flow simulations heavily depend on petrographic characterizing and modeling of reservoir rocks. Mineral phase segmentation and pore network modeling are crucial stages in micro-CT based rock modeling. The success of the pore network model (PNM) to predict petrophysical properties relies on image segmentation, image resolution and most importantly nature of rock (homogenous, complex or microporous). The pore network modeling has experienced extensive research and development during last decade, however the application of these models to a variety of naturally heterogenous reservoir rock is still a challenge. In this paper, four samples from a low permeable to tight sandstone reservoir were used to characterize their petrographic and petrophysical properties using high-resolution micro-CT imaging. The phase segmentation analysis from micro-CT images shows that 5–6% microporous regions are present in kaolinite rich sandstone (E3 and E4), while 1.7–1.8% are present in illite rich sandstone (E1 and E2). The pore system percolates without micropores in E1 and E2 while it does not percolate without micropores in E3 and E4. In E1 and E2, total MICP porosity is equal to the volume percent of macrospores determined from micro-CT images, which indicate that the macropores are well connected and microspores do not play any role in non-wetting fluid (mercury) displacement process. Whereas in E3 and E4 sandstones, the volume percent of micropores is far less (almost 50%) than the total MICP porosity which means that almost half of the pore space was not detected by the micro-CT scan. PNM behaved well in E1 and E2 where better agreement exists in PNM and MICP measurements. While E3 and E4 exhibit multiscale pore space which cannot be addressed with single scale PNM method, a multiscale approach is needed to characterize such complex rocks. This study provides helpful insights towards the application of existing micro-CT based petrographic characterization methodology to naturally complex petroleum reservoir rocks.

A Pore Scale Flow Simulation of Reconstructed Model Based on the Micro Seepage Experiment

Researches on microscopic seepage mechanism and fine description of reservoir pore structure play an important role in effective development of low and ultralow permeability reservoir. The typical micro pore structure model was established by two ways of the conventional model reconstruction method and the built-in graphics function method of Comsol® in this paper. A pore scale flow simulation was conducted on the reconstructed model established by two different ways using creeping flow interface and Brinkman equation interface, respectively. The results showed that the simulation of the two models agreed well in the distribution of velocity, pressure, Reynolds number, and so on. And it verified the feasibility of the direct reconstruction method from graphic file to geometric model, which provided a new way for diversifying the numerical study of micro seepage mechanism.

Pore scale rock typing and upscaling

Rock-typing is an important part for micro pore scale flow simulation and macro scale reservoir simulation. It is the linkage between pore geometries and fluid flow properties. Recent research advances on pore scale flow simulation enable rock properties to be calculated based on the digital images. But the calculation results doesn’t reflect the properties of whole rock sample. Therefore a suitable upscaling method is needed. In this study we first illustrate three different rock types: depositional rock type, petrographic rock type and hydraulic rock type. Depositional rock type is defined within the context of the large-scale geologic framework and represent those original rock properties present at deposition. Petrographic rock type is also described in the context of the geological framework established from the depositional rock types, but is based on a pore-scale microscopic imaging. Hydraulic rock types is also quantified on the pore scale but represent the physical rock flow and storage properties as controlled by the pore structure. Then we introduce a work flow process that accurately solves the problem of rock typing and upscaling. The reservoir rock is a thin-bedded sandstone from an aeolian environment. For petrographic rock typing, we suppose thin-bedded rock sample as a layer system and define a measurement window moving along the z -axis of the core with Δ z =1 voxel, perpendicular to the bedding direction. Minkowski functions namely total volume, surface area, integral of mean curvature, and integral of Gaussian curvature, are calculated based on the measure windows and kmeans clustering is applied to detect layer interface. Furthermore, the integration of spatial interpolation and kmeans clustering is proved to detect the dipping interface successfully. The classification results match well with corresponding properties and stratigraphic pitch-out can be found, which reflects the aeolian process, e.g., the activity of the winds to enable sediment transport. For hydraulic rock typing, the size, geometry, and distribution of pore throats, as determined by capillary pressure measurements, control the magnitude of porosity and permeability for a given rock. Therefore dynamic geometrical properties during the physical rock flow should be considered and we use percolation test data which includes critical diameter and Minkowski functions. All of these data are calculated based on the pore throats, which the fluid flows on it. The key to successful and efficient characterization is to exploit natural scales. Values and variability of each property are function of scale due to heterogeneities. Therefore, representative elementary volumes should be selected suitably to stabilize the data measurements. We first choose different sizes of subsample and measure corresponding percolation test data, permeability and effective conductivity. After selecting suitable representative elementary volumes, bottom blocks of subsamples are used for unsupervised Gaussian mixture model clustering and top blocks of subsamples are used for supervised Gaussian mixture model clustering based on the calculated centroid which means the mean value and covariance matrix of the percolation test data for each rock type in bottom blocks. The results demonstrate that different rock types are well separated with each other and match well with the corresponding geometrical properties and petrophysical properties. Three formulas which are based on layer system, undulating surfaces and hydraulic rock typing results, are developed to do upscaling. Local permeabilities and effective conductivities are computed to predict whole rock sample’s permeabilities and effective conductivities. The results indicate that upscaling formula based on the hydraulic rock typing results is most accurate.

Towards aeraulic simulations at urban scale using the lattice Boltzmann method

The lattice Boltzmann method (LBM) is an innovative approach in computational fluid dynamics (CFD). Due to the underlying lattice structure, the LBM is inherently parallel and therefore well suited for high performance computing. Its application to outdoor aeraulic studies is promising, e.g. applied on complex urban configurations, as an alternative approach to the commonplace Reynolds-averaged Navier–Stokes and large eddy simulation methods based on the Navier–Stokes equations. Emerging many-core devices, such as graphic processing units (GPUs), nowadays make possible to run very large scale simulations on rather inexpensive hardware. In this paper, we present simulation results obtained using our multi-GPU LBM solver. For validation purpose, we study the flow around a wall-mounted cube and show agreement with previously published experimental results. Furthermore, we discuss larger scale flow simulations involving nine cubes which demonstrate the practicability of CFD simulations in building external aeraulics.

Numerical Validation of Gridless Boltzmann Equation Solver

This paper describes a numerical solver of the Boltzmann equation which is originally developed for micro scale flow simulations. The convection terms are evaluated with an upwind gridless method, while the collision term is evaluated using a kinetic model collision term which correctly resembles the lower 13 moments of the Boltzmann equation. Validation of the solveris carried out for a supersonic flow over a circular cylinder at a free stream Mach number of 2.0 and several Knudsen numbers from 0.01 to 1.0. The numerical results are compared with those of the direct simulation Monte Carlo (DSMC) method and those of the compressible Navier-Stokes equations with slip boundary conditions. The comparison indicates that the results of the present Boltzmann equation solver are in good agreement with those of the DSMC method for the whole range of Knudsen number considered and the predictions of the slip Navier-Stokes equations are adequate if the Knudsen number is less than 0.1.

Parallelized FVM algorithm for three-dimensional viscoelastic flows

A parallel implementation for the finite volume method (FVM) for three-dimensional (3D) viscoelastic flows is developed on a distributed computing environment through Parallel Virtual Machine (PVM). The numerical procedure is based on the SIMPLEST algorithm using a staggered FVM discretization in Cartesian coordinates. The final discretized algebraic equations are solved with the TDMA method. The parallelisation of the program is implemented by a domain decomposition strategy, with a master/slave style programming paradigm, and a message passing through PVM. A load balancing strategy is proposed to reduce the communications between processors. The three-dimensional viscoelastic flow in a rectangular duct is computed with this program. The modified Phan-Thien–Tanner (MPTT) constitutive model is employed for the equation system closure. Computing results are validated on the secondary flow problem due to non-zero second normal stress difference N2. Three sets of meshes are used, and the effect of domain decomposition strategies on the performance is discussed. It is found that parallel efficiency is strongly dependent on the grid size and the number of processors for a given block number. The convergence rate as well as the total efficiency of domain decomposition depends upon the flow problem and the boundary conditions. The parallel efficiency increases with increasing problem size for given block number. Comparing to two-dimensional flow problems, 3D parallelized algorithm has a lower efficiency owing to largely overlapped block interfaces, but the parallel algorithm is indeed a powerful means for large scale flow simulations.